1) TWO WHICH ARE FOUR
QUESTION: The Gemara explains that Shevuos follows Makos because the Mishnah in the end of Makos says that a person receives two sets of Malkus for transgressing the Isur of shaving his head, and five sets of Malkus for transgressing the Isur of shaving his entire beard. Just as that Mishnah mentions a single sin for which a person is punished twice, the Mishnah in Shevuos mentions two prohibitions that are written in the Torah, from which a Derashah derives another two prohibitions.
What is the comparison between the Mishnah in Makos and the Mishnah here? The Mishnah in Makos discusses one prohibition for which a person is Chayav two sets of Malkus, while the Mishnah here refers to two sins which are four. The Mishnah here is more comparable to the second part of the Mishnah in Makos that says that shaving the entire beard is a single sin for which five sets of Malkus can be given. In addition, the two sets of Malkus for cutting the Pe'os ha'Rosh are equally explicit in the verse, while only two of the four sins mentioned in the Mishnah here are written explicitly!
ANSWER: The CHASAM SOFER (2b) and CHIKREI LEV answer that the Gemara in Makos (20b) teaches that we learn from "Lo Sakifu" (Vayikra 19:27) that the person who is shaved also transgresses the Lav. Therefore, if a person moves his head while being shaved to facilitate the haircut, he is Chayav Malkus. If a person shaves his own hair, he is Chayav two sets of Malkus -- one for cutting it, and one for having it cut. According to this, the Isur of cutting the two Pe'os ha'Rosh is also an Isur that involves two explicit Isurim (the two Pe'os) which are four according to the Derashah (two for the Makif and two for the Nikaf), and it is identical to the other Isurim that are described as "two which are four" in the Mishnah. (By placing Shevuos after Makos, the Mishnah hints to what the Beraisa teaches in Makos (20b); the Isur of cutting the Pe'os ha'Rosh is "two Isurim which are really four," since it includes the Isur of being Nikaf as well.)

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2) THE TANA OF THE MISHNAH
QUESTION: The Gemara attempts to determine which Tana is the author of the Mishnah. It suggests that the Mishnah is the view of Rebbi Yishmael, who maintains that one is obligated to bring a Korban both for He'elem Tum'ah and for He'elem Mikdash, which is the view expressed in the Mishnah. However, Rebbi Yishmael does not obligate a person to bring a Korban for a Shevu'as Sheker when he swears falsely that an action occurred in the past. If Rebbi Yishmael is the author of the Mishnah, then why does the Mishnah say that there are four Shevu'os ("two which are four") for which one is Chayav, including two Shevu'os regarding the past?
The Gemara suggests that the Mishnah is discussing the liability for Malkus and not the obligation to bring a Korban, as Rava teaches. Rava says that just as the Torah obligates Malkus for a Shevu'as Shav (with the word "Lo Yenakeh," Shemos 20:7), it also obligates Malkus for a Shevu'as Sheker made for a past event. The Gemara challenges this answer, because even Rava agrees that Malkus is not given to a person who swears that he will do something in the future and he does not do that thing, since it is a Lav she'Ein Bo Ma'aseh. The Gemara answers that Rebbi Yishmael maintains that Malkus is given for a Lav she'Ein Bo Ma'aseh, and that is why he would obligate Malkus for a person who does not fulfill his Shevu'ah to perform an action in the future.
There are a number of difficulties with this Gemara.
1. Why does the Gemara cite Rava to prove that Malkus is given for a Shevu'as Sheker, a false oath? Rava's teaching is not the source for Malkus for a Shevu'as Sheker! Rather, it is learned from Rebbi Yochanan's Derashah: the Torah includes Shevu'as Sheker in the Aseres ha'Dibros by writing the word "la'Shav" (Shemos 20:7) a second time. Therefore, the words "Lo Yenakeh" in that verse teach that a Shevu'as Sheker is also punishable with Malkus. Rava's teaching is not cited as the source for Malkus for a Shevu'as Sheker, but rather his teaching exempts a person who makes a Shevu'as Sheker about the future from receiving Malkus (since a Shevu'as Sheker is not similar to a Shevu'as Shav, which involves only a matter of the past).
Rava's statement raises a difficulty with asserting that the Mishnah follows the view of Rebbi Yishmael, because Rava makes it clear that not every Shevu'ah is punished with Malkus. (TOSFOS DH veched'Rava)
2. According to the Gemara's conclusion that Rebbi Yishmael maintains that one receives Malkus for a Lav she'Ein Bo Ma'aseh, the teaching of Rava is no longer needed as a source that one receives Malkus for a Shevu'as Sheker. Rather, Malkus will be given because it is a Lav she'Ein Bo Ma'aseh. Why, then, does the Gemara not precede this answer with the word "Ela" ("rather"), which denotes the beginning of a new answer? (See MAHARSHA.)
3. According to the Gemara's conclusion, all punishments of Malkus given for all Shevu'os are based on the same principle -- that Malkus is administered for a Lav she'Ein Bo Ma'aseh. Why, then, does the Mishnah group the Shevu'os as "two which are four"? The punishments of Malkus for the first two Shevu'os (which are l'Haba, regarding the future) are just as explicit as those for the other two Shevu'os (regarding the past)!
With regard to the obligation to bring a Korban, the Mishnah has good reason to list the Shevu'os regarding the future separately, since the verse that discusses the obligation to bring a Korban (Vayikra 5:4) mentions only this type of Shevu'ah (Shevu'ah l'Haba). However, with regard to Malkus, there is a specific Lav for Shevu'ah leshe'Avar (regarding the past) in the verse, "v'Lo Sishav'u" (Vayikra 19:12), and with regard to a Shevu'ah l'Haba there is an explicit Lav in the verse, "Lo Yachel Devaro" (Bamidbar 30:3). All of the four Shevu'os, therefore, should be equal! (See TOSFOS DH Aval, RITVA, and TOSFOS HA'ROSH.)
ANSWERS:
(a) RABEINU CHANANEL, TOSFOS (DH Aval), and the RASHBA explain that when the Gemara says that Rebbi Yishmael maintains that one receives Malkus for a Lav she'Ein Bo Ma'aseh, it does not mean that Rebbi Yishmael always gives Malkus for a Lav she'Ein Bo Ma'aseh (like the view of Rebbi Yehudah). Rather, Rebbi Yishmael administers Malkus only for the Isur of a Shevu'as Bituy, even when it does not involve a Ma'aseh (for example, he makes a Shevu'ah that he will eat, and then he does not eat). Rebbi Yishmael derives this from the extra word "la'Shav" in the verse "Lo Yenakeh" (Shemos 20:7), as Rebbi Yochanan teaches. (This approach avoids the contradiction between the Gemara here and the Gemara in Makos (13b) with regard to whether Rebbi Yishmael administers Malkus for a Lav she'Ein Bo Ma'aseh. See Rashi, DH Kashya.) This approach answers the questions as follows:
1. There are two opinions that obligate Malkus for a Shevu'as Bituy, even though a Lav she'Ein Bo Ma'aseh normally is not punishable with Malkus. The first opinion is expressed by Rava, who derives from "la'Shav" that one is Chayav Malkus for a Shevu'as Bituy regarding the past. One who does not accept Rava's argument may follow the second opinion, according to the teaching of Rebbi Yochanan, that one can be Chayav Malkus for a Shevu'as Bituy regarding both the past and the future.
Rebbi Yishmael must follow one of these two opinions. However, each opinion has a disadvantage. Originally, the Gemara suggests that Rebbi Yishmael follows the view of Rava, because there is a disadvantage to saying that he maintains that all Shevu'os Bituy are punishable with Malkus, since there would be no reason for the Mishnah to divide the Shevu'os into two sets, "two which are four" (as the third question above expresses). Later, the Gemara rejects this approach, because, according to Rava, Malkus is not given at all for a Shevu'ah l'Haba, a Shevu'ah regarding the future, and therefore the Gemara is left with the position that Rebbi Yishmael maintains that Malkus is given for all Shevu'os Bituy because of Rebbi Yochanan's teaching.
2. The Gemara should have used the word "Ela" since it is changing its position entirely. Why does it not say "Ela"? (See MAHARSHA.) The RITVA explains that the Gemara does not always use the word "Ela" even when it starts a new answer. TOSFOS also uses this approach in many places where the original answer of the Gemara was not given in the name of any Amora (see Yevamos 27a, DH Shmuel, and Shabbos 105b, DH Havah Amina).
3. TOSFOS (DH Aval) explains that the Mishnah divides the Shevu'os into two groups, because the Shevu'os l'Haba are written more explicitly with regard to the obligation to bring a Korban, even though it is mentioned in the Mishnah only in the context of Malkus (according the Gemara's initial assumption). Similar logic applies even if the Mishnah refers to the Korban that is brought for making such Shevu'os. Why should the Mishnah refer to the Shevu'os that one made with regard to having done or not done something in the past as two separate categories? In both cases, the Shevu'ah is false as soon as it leaves the person's mouth, because he did not actually do or not do what he said. The only reason the Mishnah distinguishes between the two is that the verse makes such a distinction regarding Shevu'ah l'Haba ("l'Ha'ra O l'Heitiv"). (See Tosfos there for another answer in the name of the RITZBA.)
According to Tosfos and Rabeinu Chananel, why does the Gemara later try to prove that Malkus is not given for a Lav she'Ein Bo Ma'aseh from the Mishnah which says that Malkus is not given for the Isur of ha'Mosir, one who leaves over the Korban Pesach? Since that Mishnah is not discussing Shevu'ah, even Rebbi Yishmael agrees that Malkus is not given when there is no Ma'aseh! (MAHARSHA)
Apparently, Tosfos understands that the Gemara indeed could have pointed that out, but instead it chose to give another reason to reject the proof from the Mishnah regarding ha'Mosir.
(b) The RITVA suggests another approach. Indeed, Rebbi Yishmael maintains that Malkus is given for every Lav she'Ein Bo Ma'aseh. Why, then, does the Mishnah divide the Shevu'os into two groups, "two which are four"? The reason is that Malkus for Shevu'os regarding the past is written explicitly in the verse that says "Lo Yenakeh" which refers to Shevu'as Shav and Shevu'as Sheker leshe'Avar. The Malkus for a Shevu'ah Sheker l'Haba is not written explicitly, but rather is derived from the verse of "Lo Sachsom" (Devarim 25:3-4; see Makos 13b) which teaches that Malkus is given for all Lavim, including the transgression of a Shevu'ah.
This answers the questions as follows:
1. The Gemara cites Rava in order to show that only with regard to a Shevu'ah about the past does the verse explicitly prescribe Malkus. That is why the Mishnah divides the Shevu'os into two groups, "two which are four."
2. The Gemara does not say "Ela" when it proposes that Rebbi Yishmael gives Malkus for every Lav she'Ein Bo Ma'aseh, because the teaching of Rava is still needed to teach that the Malkus for a Shevu'ah about the past is written more explicitly that the Malkus for a Shevu'ah about the future.
3. The reason why the Mishnah divides the Shevu'os into two groups is that the Malkus for Shevu'os about the past is written explicitly.
The problem with this approach is that the Mishnah later (19b) explains that the phrase "two Shevu'os which are four" refers first to the two Shevu'os regarding the future, and then to the additional two Shevu'os regarding the past. The sequence of the Mishnah implies that the "two" of the Mishnah are the Shevu'os regarding the future, and not the Shevu'os regarding the past. The Ritva writes that according to this approach, although the Mishnah here refers to Malkus, the Mishnah later (19b) refers to "two Shevu'os which are four" with regard to Korban, and it is following the opinion of Rebbi Akiva.
(c) The TOSFOS HA'ROSH and the RAV ABAD (cited by the RAN) explain that since the Torah specifies with regard to Korban that a Korban is brought only for a Shevu'ah about the future, one would have concluded that even with regard to Malkus the Torah prohibits a Shevu'as Sheker only when it is about the future, since the Torah does not mention a Shevu'ah about the past explicitly. It is only from the verse of "la'Shav" that one learns that the Isur of Shevu'as Sheker applies also to the past.
The Gemara is forced to take this approach since, otherwise, there would be no reason for the Mishnah to divide the Shevu'os into two groups. The RITVA also offers this as an alternate solution.
This answers the questions as follows:
1. The Gemara cites Rava to show that the verse of "la'Shav" specifically refers to a Shevu'ah about the past since, without that verse, one would not know that a Shevu'ah about the past is included in the Isur of Shevu'as Sheker.
2. The Gemara does not say "Ela" when it concludes that Rebbi Yishmael administers Malkus for every Lav she'Ein Bo Ma'aseh, since the teaching of Rava is still needed to show that the Isur of Shevu'as Sheker also includes swearing falsely about the past.
3. The reason why the Mishnah divides the Shevu'os into two groups, "two which are four," is that the Shevu'ah l'Haba is written explicitly in the verse. However, the fact that a Shevu'ah about the past is prohibited is known only from the Derashah of the extra word "la'Shav."

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